Definition 2.14 The cup product \([Z]\cup -\)  defines a nilpotent endomorphism with index \((m+1)\)  on the total cohomology \(H^*(Y,\mathbb {Q})\) . By [1]}, it therefore defines an increasing weight filtration on \(H^*(Y,\mathbb {Q})\) , centred at \(n\) . We call this filtration the cup-product filtration and denote it by \(K_{\bullet }\) .

